Time-Varying Graph Signal Estimation among Multiple Sub-Networks

TL;DR

This paper introduces a cooperative Kalman filter approach for estimating time-varying signals across multiple sub-networks in sensor networks, reducing resource use by transferring learned models between clusters.

Contribution

It proposes a novel method combining Kalman filtering and optimal transport to estimate signals across sub-networks with different sizes, enhancing efficiency.

Findings

Effective in synthetic signal experiments

Validated on real-world sensor data

Reduces resource consumption in large networks

Abstract

This paper presents an estimation method for time-varying graph signals among multiple sub-networks. In many sensor networks, signals observed are associated with nodes (i.e., sensors), and edges of the network represent the inter-node connectivity. For a large sensor network, measuring signal values at all nodes over time requires huge resources, particularly in terms of energy consumption. To alleviate the issue, we consider a scenario that a sub-network, i.e., cluster, from the whole network is extracted and an intra-cluster analysis is performed based on the statistics in the cluster. The statistics are then utilized to estimate signal values in another cluster. This leads to the requirement for transferring a set of parameters of the sub-network to the others, while the numbers of nodes in the clusters are typically different. In this paper, we propose a cooperative Kalman filter between two sub-networks. The proposed method alternately estimates signals in time between two sub-networks. We formulate a state-space model in the source cluster and transfer it to the target cluster on the basis of optimal transport. In the signal estimation experiments of synthetic and real-world signals, we validate the effectiveness of the proposed method.